General:
* Tropical forest
* Jungle (though this can be considered informal)
* Equatorial forest
* Hygrotropic forest (emphasizes its high humidity)
* Rainforest biome
* Tropical rainforest (if you want to emphasize the climate)
More specific:
* Amazon rainforest (referring specifically to the Amazon)
* Congo rainforest (referring specifically to the Congo basin)
* Daintree Rainforest (referring specifically to the Daintree Rainforest in Australia)
* Cloud forest (a type of rainforest found at higher altitudes)
* Montane forest (another term for cloud forest)
The best word will depend on the context.